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Resume On montre, par adaptation d'une méthode proposée par L. TARTAR, que pour le problème modèle — ɛ Δ uɛ+uɛ=u dans un ouvert Ω, uɛ=O au bord de Ω certaines estimations gobales valables quand u ε Ho1(Ω), donc quand il n'y a pas de couche limite ont des analogues dans des ouverts intérieurs à Ω quand u ε Hloc1 (Ω) donc quand il y a couche...
Résumé La technique des développements asymptotiques raccordés est utilisée pour étudier les écoulements subsoniques à grand nombre de Reynolds autour des ailes minces, dans le cas où l'épaisseur de couche limite est très faible devant le rayon de courbure du bord d'attaque. L'approximation de fluide parfait s'écrit sous la forme d'une solution extérieure qui n'est autre que la solution classique...
On voit, d'après son mode de formation (voir § 5. a)), que la condition de structure d'ordre ⓝ fait intervenir les dérivées des Tj par rapport à leurs arguments φ,k jusqu'à l'ordre n+2. L'ensemble des conditions de structure d'ordre inférieur ou égal à ⓝ caractérise la classe des équations de conservation qui sont modulables jusqu'à l'ordre ⓝ au moins, lorsqu'elles possèdent des familles d'ondes planes...
A layer of viscous fluid lying between two heated horizontal, parallel plates is considered. When a critical adverse temperature gradient is established across the layer, heat is no longer transferred by conduction alone, and a convective motion is established. We model this physical phenomenon with the Boussinesq approximation to the Navier-Stokes equations, and using this mathematical model, we...
The purpose of this paper is to develop an asymptotic theory for the core of a tightly winded rolled vortex sheet, when winding arises around a line. The physical picture replaces the core by a region of distributed vorticity, the so-called vortex filament. The (pseudo) mathematical picture relies on an algorithm which allows to relate (in a quite convincing but non rigorous way) a flow with vorticity...
A technique is developed to obtain non-similar solutions of the laminar boundary layer equations governing the recirculating flow behind a finite base. The solutions are represented as expansions in powers of the dimensionless base height. The Chapman similarity solution is the first term in this expansion. The technique is applied to the calculation of recirculating flow behind the base of a two...
Systems of difference equations containing small parameters are studied by a constructive perturbation scheme analogous to the one developed by the authors for the study of differential equations. The method results in an averaging procedure for difference equations, and it is particularly well suited to certain highly oscillatory, nonlinear systems. The method is applied to problems from population...
Conclusion Nous avons étudié les phénomènes acoustiques dans un milieu poreux comme un problème à un petit paramètre ℓ/L, le rapport de la dimension des pores à une longueur caractéristique des phénomènes macroscopiques. L'hypothèse fondamentale est que les nombres sans dimension RR et A sont de l'ordre de 1, ce qui revient à dire que dans l'écoulement microscopique les termes de dissipation sont...
The motion of a compressible viscous gas in a rapidly rotating cylinder closed at both ends is investigated by the linear theory. The rigid rotation state is perturbed slightly by source or sinks and by thermal gradients. The method of matched asymptotic expansions is used to find uniform solutions in powers of the Ekman number. In the Stewartson 1/3 layer along the side wall, the Ekman number ε at...
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